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Title:
On the final exponentiation for calculating pairings on ordinary elliptic curves
Authors: Michael Scott, Naomi Benger, Manuel Charlemagne, Luis J. Dominguez Perez, Ezekiel J. Kachisa
Abstract:When using pairing-friendly ordinary elliptic curves to compute the Tate and related pairings, the computation consists of two main components, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of ``truncated loop’’ pairings like the R-ate pairing), the final exponentiation has become a more significant component of the overall calculation. Here we exploit the structure of pairing friendly elliptic curves to reduce the computation required for the final exponentiation to a minimum.
ePrint: https://eprint.iacr.org/2008/490
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